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Fibonacci oscillators

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Zeitschrift für Physik C Particles and Fields

Abstract

We discuss the properties of oscillators whose spectrum is given by a generalized Fibonacci sequence. The properties include: invariance under the unitary quantum group, generalized angular momentum, coherent states and difference calculus, relativistic interpretation.

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References

  1. L.D. Fadeev, N.Y. Reshetikhin, L.A. Takhtajan: Quantization of Lie groups and Lie algebras, preprint LOMI, 1987; V.G. Drinfeld: Quantum groups, Proc. Int. Congr. Math., Berkeley 1 (1986) 798–820; M. Jimbo: Lett. Math. Phys. 11 (1986) 247; S.L. Woronowicz: Commun. Math. Phys. 111 (1987) 613

  2. A. Mcfarlane: J. Phys. A 22 (1989) 4581

    Google Scholar 

  3. A. Biedenharn: J. Phys. A 22 (1989) L873

    Google Scholar 

  4. M. Chaichian, P. Kulish: Phys. Lett. B234 (1990) 72

    Google Scholar 

  5. P. Kulish, E. Damaskinsky: J. Phys. A 23 (1990) L415

    Google Scholar 

  6. W. Pusz, S.L. Woronowicz: Rep. Math. Phys. 27 (1989) 231

    Google Scholar 

  7. M. Arik: Z. Phys. C—Particles and Fields 51 (1991) 627

    Google Scholar 

  8. F.H. Jackson, Q.J. Pure: Appl. Math. 41 (1910) 193

    Google Scholar 

  9. J. Wess, B. Zumino: Covariant differential cacculus on the quantum hyperplane, CERN preprint TH-5697/90 (1990). To be published in Nucl. Phys. B

  10. M. Arik, D.D. Coon: J. Math. Phys. 17 (1975) 524

    Google Scholar 

  11. M. Baker, D.D. Coon, S. Yu: Phys. Rev. D5 (1972) 1429; S.Yu: Phys. Rev. D7 (1973) 1871; Nuovo Cimento 28A (1975) 203; M. Arik, D.D. Coon, Y.M. Lam: J. Math. Phys. 16 (1975) 1776

    Google Scholar 

  12. M. Bicknell, V.E. Hoggatt, Jr. (eds.): A primer for the Fibonacci numbers, reprint of articles published in the Fibonacci Quarterly, The Fibonacci Associaton. San Jose: San Jose: San Jose State University Press 1972

    Google Scholar 

  13. R. Charkrabarti, R. Jagannathan: J. Phys. A (1991) L 711; G. Brodimas, A. Jannussis, R. Mignani: Two parameter quantum groups, Universita di Roma, preprint Nr. 820, 1991

  14. R.W. Gray, C.A. Nelson: J. Phys. A23 (1990) L945; A.J. Bracken, D.S. Anally, R.B. Zhang, M.D. Gould: J. Phys. A24 (1991) 1379; B. Jurco: Lett. Math. Phys. 21 (1991) 51

    Google Scholar 

  15. M. Arik, M. Mungan:q-Oscillators and relativistic position operators. Istanbul Technical Univ. preprint (1991), to be published in Phys. Lett. B

  16. R.M. Mir-Kasimov: J. Phys. A24 (1991) 4283; R.M. Mir-Kasimov, E. Kogramanov, Sh. Nagiev: J. Math. Phys. 31 (1990) 1733

    Google Scholar 

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Author notes

  1. T. Turgut

    Present address: Department of Physics, University of Rochester, Rochester, NY, USA

  2. M. Mungan

    Present address: Department of Physics, University of Chicago, Chicago, Ill., USA

Authors and Affiliations

  1. Department of Mathematics, Istanbul Technical University, Maslak, Istanbul, Turkey

    M. Arik

  2. Department of Physics, Bogaziçi University, Bebek, Istanbul, Turkey

    M. Arik

  3. Department of Physics, University of Texas at Austin, Austin, Texas, USA

    E. Demircan & T. Turgut

  4. Department of Physics, Bogaziçi University, Bebek, Istanbul, Turkey

    L. Ekinci & M. Mungan

Authors
  1. M. Arik
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  2. E. Demircan
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  3. T. Turgut
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  4. L. Ekinci
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  5. M. Mungan
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Arik, M., Demircan, E., Turgut, T. et al. Fibonacci oscillators. Z. Phys. C - Particles and Fields 55, 89–95 (1992). https://doi.org/10.1007/BF01558292

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  • DOI: https://doi.org/10.1007/BF01558292

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